The Hasse principle for pairs of diagonal cubic forms
arXiv:0710.4778 · doi:10.4007/annals.2007.166.865
Abstract
By means of the Hardy-Littlewood method, we apply a new mean value theorem for exponential sums to confirm the truth, over the rational numbers, of the Hasse principle for pairs of diagonal cubic forms in thirteen or more variables.
Accepted to appear in Annals of Mathematics, 9th September 2005
Cited by in corpus (12)
- Rational solutions of pairs of diagonal equations, one cubic and one quadratic
- Sums of three cubes, II
- Systems of cubic forms in many variables
- Davenport's method and slim exceptional sets: the asymptotic formulae in Waring's problem
- Systems of forms in many variables
- Simultaneous additive equations: Repeated and differing degrees
- Arithmetic harmonic analysis for smooth quartic Weyl sums: three additive equations
- Correlation estimates for sums of three cubes
- The Hasse principle for systems of diagonal cubic forms
- Subconvexity for additive equations: pairs of undenary cubic forms
- Integral solutions to systems of diagonal equations
- Cubic moments of Fourier coefficients and pairs of diagonal quartic forms